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RFC 2945 - The SRP Authentication and Key Exchange System

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Network Working Group                                              T. Wu
Request for Comments: 2945                           Stanford University
Category: Standards Track                                 September 2000

             The SRP Authentication and Key Exchange System

Status of this Memo

   This document specifies an Internet standards track protocol for the
   Internet community, and requests discussion and suggestions for
   improvements.  Please refer to the current edition of the "Internet
   Official Protocol Standards" (STD 1) for the standardization state
   and status of this protocol.  Distribution of this memo is unlimited.

Copyright Notice

   Copyright (C) The Internet Society (2000).  All Rights Reserved.


   This document describes a cryptographically strong network
   authentication mechanism known as the Secure Remote Password (SRP)
   protocol.  This mechanism is suitable for negotiating secure
   connections using a user-supplied password, while eliminating the
   security problems traditionally associated with reusable passwords.
   This system also performs a secure key exchange in the process of
   authentication, allowing security layers (privacy and/or integrity
   protection) to be enabled during the session.  Trusted key servers
   and certificate infrastructures are not required, and clients are not
   required to store or manage any long-term keys.  SRP offers both
   security and deployment advantages over existing challenge-response
   techniques, making it an ideal drop-in replacement where secure
   password authentication is needed.

1. Introduction

   The lack of a secure authentication mechanism that is also easy to
   use has been a long-standing problem with the vast majority of
   Internet protocols currently in use.  The problem is two-fold: Users
   like to use passwords that they can remember, but most password-based
   authentication systems offer little protection against even passive
   attackers, especially if weak and easily-guessed passwords are used.

   Eavesdropping on a TCP/IP network can be carried out very easily and
   very effectively against protocols that transmit passwords in the
   clear.  Even so-called "challenge-response" techniques like the one
   described in [RFC 2095] and [RFC 1760], which are designed to defeat

   simple sniffing attacks, can be compromised by what is known as a
   "dictionary attack".  This occurs when an attacker captures the
   messages exchanged during a legitimate run of the protocol and uses
   that information to verify a series of guessed passwords taken from a
   precompiled "dictionary" of common passwords.  This works because
   users often choose simple, easy-to-remember passwords, which
   invariably are also easy to guess.

   Many existing mechanisms also require the password database on the
   host to be kept secret because the password P or some private hash
   h(P) is stored there and would compromise security if revealed.  That
   approach often degenerates into "security through obscurity" and goes
   against the UNIX convention of keeping a "public" password file whose
   contents can be revealed without destroying system security.

   SRP meets the strictest requirements laid down in [RFC 1704] for a
   non-disclosing authentication protocol.  It offers complete
   protection against both passive and active attacks, and accomplishes
   this efficiently using a single Diffie-Hellman-style round of
   computation, making it feasible to use in both interactive and non-
   interactive authentication for a wide range of Internet protocols.
   Since it retains its security when used with low-entropy passwords,
   it can be seamlessly integrated into existing user applications.

2. Conventions and Terminology

   The protocol described by this document is sometimes referred to as
   "SRP-3" for historical purposes.  This particular protocol is
   described in [SRP] and is believed to have very good logical and
   cryptographic resistance to both eavesdropping and active attacks.

   This document does not attempt to describe SRP in the context of any
   particular Internet protocol; instead it describes an abstract
   protocol that can be easily fitted to a particular application.  For
   example, the specific format of messages (including padding) is not
   specified.  Those issues have been left to the protocol implementor
   to decide.

   The one implementation issue worth specifying here is the mapping
   between strings and integers.  Internet protocols are byte-oriented,
   while SRP performs algebraic operations on its messages, so it is
   logical to define at least one method by which integers can be
   converted into a string of bytes and vice versa.

   An n-byte string S can be converted to an integer as follows:

   i = S[n-1] + 256 * S[n-2] + 256^2 * S[n-3] + ... + 256^(n-1) * S[0]

   where i is the integer and S[x] is the value of the x'th byte of S.
   In human terms, the string of bytes is the integer expressed in base
   256, with the most significant digit first.  When converting back to
   a string, S[0] must be non-zero (padding is considered to be a
   separate, independent process).  This conversion method is suitable
   for file storage, in-memory representation, and network transmission
   of large integer values.  Unless otherwise specified, this mapping
   will be assumed.

   If implementations require padding a string that represents an
   integer value, it is recommended that they use zero bytes and add
   them to the beginning of the string.  The conversion back to integer
   automatically discards leading zero bytes, making this padding scheme
   less prone to error.

   The SHA hash function, when used in this document, refers to the
   SHA-1 message digest algorithm described in [SHA1].

3. The SRP-SHA1 mechanism

   This section describes an implementation of the SRP authentication
   and key-exchange protocol that employs the SHA hash function to
   generate session keys and authentication proofs.

   The host stores user passwords as triplets of the form

        { <username>, <password verifier>, <salt> }

   Password entries are generated as follows:

        <salt> = random()
        x = SHA(<salt> | SHA(<username> | ":" | <raw password>))
        <password verifier> = v = g^x % N

   The | symbol indicates string concatenation, the ^ operator is the
   exponentiation operation, and the % operator is the integer remainder
   operation.  Most implementations perform the exponentiation and
   remainder in a single stage to avoid generating unwieldy intermediate
   results.  Note that the 160-bit output of SHA is implicitly converted
   to an integer before it is operated upon.

   Authentication is generally initiated by the client.

      Client                             Host
     --------                           ------
      U = <username>              -->
                                     <--    s = <salt from passwd file>

   Upon identifying himself to the host, the client will receive the
   salt stored on the host under his username.

      a = random()
      A = g^a % N                 -->
                                         v = <stored password verifier>
                                         b = random()
                                  <--    B = (v + g^b) % N

      p = <raw password>
      x = SHA(s | SHA(U | ":" | p))

      S = (B - g^x) ^ (a + u * x) % N    S = (A * v^u) ^ b % N
      K = SHA_Interleave(S)              K = SHA_Interleave(S)
      (this function is described
       in the next section)

   The client generates a random number, raises g to that power modulo
   the field prime, and sends the result to the host.  The host does the
   same thing and also adds the public verifier before sending it to the
   client.  Both sides then construct the shared session key based on
   the respective formulae.

   The parameter u is a 32-bit unsigned integer which takes its value
   from the first 32 bits of the SHA1 hash of B, MSB first.

   The client MUST abort authentication if B % N is zero.

   The host MUST abort the authentication attempt if A % N is zero.  The
   host MUST send B after receiving A from the client, never before.

   At this point, the client and server should have a common session key
   that is secure (i.e. not known to an outside party).  To finish
   authentication, they must prove to each other that their keys are

        M = H(H(N) XOR H(g) | H(U) | s | A | B | K)
                                    <--    H(A | M | K)

   The server will calculate M using its own K and compare it against
   the client's response.  If they do not match, the server MUST abort
   and signal an error before it attempts to answer the client's
   challenge.  Not doing so could compromise the security of the user's

   If the server receives a correct response, it issues its own proof to
   the client.  The client will compute the expected response using its
   own K to verify the authenticity of the server.  If the client
   responded correctly, the server MUST respond with its hash value.

   The transactions in this protocol description do not necessarily have
   a one-to-one correspondence with actual protocol messages.  This
   description is only intended to illustrate the relationships between
   the different parameters and how they are computed.  It is possible,
   for example, for an implementation of the SRP-SHA1 mechanism to
   consolidate some of the flows as follows:

        Client                             Host
       --------                           ------
        U, A                        -->
                                    <--    s, B
        H(H(N) XOR H(g) | H(U) | s | A | B | K)
                                    <--    H(A | M | K)

   The values of N and g used in this protocol must be agreed upon by
   the two parties in question.  They can be set in advance, or the host
   can supply them to the client.  In the latter case, the host should
   send the parameters in the first message along with the salt.  For
   maximum security, N should be a safe prime (i.e. a number of the form
   N = 2q + 1, where q is also prime).  Also, g should be a generator
   modulo N (see [SRP] for details), which means that for any X where 0
   < X < N, there exists a value x for which g^x % N == X.

3.1.  Interleaved SHA

   The SHA_Interleave function used in SRP-SHA1 is used to generate a
   session key that is twice as long as the 160-bit output of SHA1.  To
   compute this function, remove all leading zero bytes from the input.
   If the length of the resulting string is odd, also remove the first
   byte.  Call the resulting string T.  Extract the even-numbered bytes
   into a string E and the odd-numbered bytes into a string F, i.e.

     E = T[0] | T[2] | T[4] | ...
     F = T[1] | T[3] | T[5] | ...

   Both E and F should be exactly half the length of T.  Hash each one
   with regular SHA1, i.e.

     G = SHA(E)
     H = SHA(F)

   Interleave the two hashes back together to form the output, i.e.

     result = G[0] | H[0] | G[1] | H[1] | ... | G[19] | H[19]

   The result will be 40 bytes (320 bits) long.

3.2.  Other Hash Algorithms

   SRP can be used with hash functions other than SHA.  If the hash
   function produces an output of a different length than SHA (20
   bytes), it may change the length of some of the messages in the
   protocol, but the fundamental operation will be unaffected.

   Earlier versions of the SRP mechanism used the MD5 hash function,
   described in [RFC 1321].  Keyed hash transforms are also recommended
   for use with SRP; one possible construction uses HMAC [RFC 2104],
   using K to key the hash in each direction instead of concatenating it
   with the other parameters.

   Any hash function used with SRP should produce an output of at least
   16 bytes and have the property that small changes in the input cause
   significant nonlinear changes in the output.  [SRP] covers these
   issues in more depth.

4. Security Considerations

   This entire memo discusses an authentication and key-exchange system
   that protects passwords and exchanges keys across an untrusted
   network.  This system improves security by eliminating the need to
   send cleartext passwords over the network and by enabling encryption
   through its secure key-exchange mechanism.

   The private values for a and b correspond roughly to the private
   values in a Diffie-Hellman exchange and have similar constraints of
   length and entropy.  Implementations may choose to increase the
   length of the parameter u, as long as both client and server agree,
   but it is not recommended that it be shorter than 32 bits.

   SRP has been designed not only to counter the threat of casual
   password-sniffing, but also to prevent a determined attacker equipped
   with a dictionary of passwords from guessing at passwords using
   captured network traffic.  The SRP protocol itself also resists
   active network attacks, and implementations can use the securely
   exchanged keys to protect the session against hijacking and provide

   SRP also has the added advantage of permitting the host to store
   passwords in a form that is not directly useful to an attacker.  Even
   if the host's password database were publicly revealed, the attacker
   would still need an expensive dictionary search to obtain any
   passwords.  The exponential computation required to validate a guess
   in this case is much more time-consuming than the hash currently used
   by most UNIX systems.  Hosts are still advised, though, to try their
   best to keep their password files secure.

5. References

   [RFC 1321]  Rivest, R., "The MD5 Message-Digest Algorithm", RFC 1321,
               April 1992.

   [RFC 1704]  Haller, N. and R. Atkinson, "On Internet Authentication",
               RFC 1704, October 1994.

   [RFC 1760]  Haller, N., "The S/Key One-Time Password System", RFC
               1760, Feburary 1995.

   [RFC 2095]  Klensin, J., Catoe, R. and P. Krumviede, "IMAP/POP
               AUTHorize Extension for Simple Challenge/Response", RFC
               2095, January 1997.

   [RFC 2104]  Krawczyk, H., Bellare, M. and  R. Canetti, "HMAC: Keyed-
               Hashing for Message Authentication", RFC 2104, February

   [SHA1]      National Institute of Standards and Technology (NIST),
               "Announcing the Secure Hash Standard", FIPS 180-1, U.S.
               Department of Commerce, April 1995.

   [SRP]       T. Wu, "The Secure Remote Password Protocol", In
               Proceedings of the 1998 Internet Society Symposium on
               Network and Distributed Systems Security, San Diego, CA,
               pp. 97-111.

6. Author's Address

   Thomas Wu
   Stanford University
   Stanford, CA 94305

   EMail: tjw@cs.Stanford.EDU

7.  Full Copyright Statement

   Copyright (C) The Internet Society (2000).  All Rights Reserved.

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